mlsanityData to 14 Oct 2026

Marrying Causal Representation Learning with Dynamical Systems for Science

arXiv 2405.13888 ↗First posted 22 May 2024cs.LG stat.MLcited by 23

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Abstract (arXiv)

Causal representation learning promises to extend causal models to hidden causal variables from raw entangled measurements. However, most progress has focused on proving identifiability results in different settings, and we are not aware of any successful real-world application. At the same time, the field of dynamical systems benefited from deep learning and scaled to countless applications but does not allow parameter identification. In this paper, we draw a clear connection between the two and their key assumptions, allowing us to apply identifiable methods developed in causal representation learning to dynamical systems. At the same time, we can leverage scalable differentiable solvers developed for differential equations to build models that are both identifiable and practical. Overall, we learn explicitly controllable models that isolate the trajectory-specific parameters for further downstream tasks such as out-of-distribution classification or treatment effect estimation. We experiment with a wind simulator with partially known factors of variation. We also apply the resulting model to real-world climate data and successfully answer downstream causal questions in line with existing literature on climate change.

Key facts. Cited by 23 papers in the map (data through 14 Oct 2026). Builds on 44 of its 74 references that are in the map. First posted on arXiv 22 May 2024.

Builds on

44 of 74 references.

References · 44

  1. 2018Neural Ordinary Differential Equationscited by 3,779
  2. 2018Challenging Common Assumptions in the Unsupervised Learning of Disentangled Representationscited by 941
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  4. 2021Self-Supervised Learning with Data Augmentations Provably Isolates Content from Stylecited by 312
  5. 2020Weakly-Supervised Disentanglement Without Compromisescited by 239
  6. 2021Contrastive Learning Inverts the Data Generating Processcited by 221
  7. 2021Disentanglement via Mechanism Sparsity Regularization: A New Principle for Nonlinear ICAcited by 160
  8. 2022Interventional Causal Representation Learningcited by 142
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  12. 2020Towards Nonlinear Disentanglement in Natural Data with Temporal Sparse Codingcited by 122
32 more
  1. 2023Nonparametric Identifiability of Causal Representations from Unknown Interventionscited by 106
  2. 2023Learning Linear Causal Representations from Interventions under General Nonlinear Mixingcited by 92
  3. 2022Linear Causal Disentanglement via Interventionscited by 84
  4. 2023Identifiability Guarantees for Causal Disentanglement from Soft Interventionscited by 84
  5. 2023Multi-View Causal Representation Learning with Partial Observabilitycited by 74
  6. 2022Identifiability of deep generative models without auxiliary informationcited by 70
  7. 2020On Second Order Behaviour in Augmented Neural ODEscited by 68
  8. 2022Weakly Supervised Representation Learning with Sparse Perturbationscited by 65
  9. 2023ODEFormer: Symbolic Regression of Dynamical Systems with Transformerscited by 62
  10. 2022Temporally Disentangled Representation Learningcited by 61
  11. 2023Identifiability Results for Multimodal Contrastive Learningcited by 61
  12. 2023Additive Decoders for Latent Variables Identification and Cartesian-Product Extrapolationcited by 58
  13. 2021Identifiable Deep Generative Models via Sparse Decodingcited by 54
  14. 2022Causal Representation Learning for Instantaneous and Temporal Effects in Interactive Systemscited by 51
  15. 2022Synergies between Disentanglement and Sparsity: Generalization and Identifiability in Multi-Task Learningcited by 44
  16. 2021Understanding Latent Correlation-Based Multiview Learning and Self-Supervision: An Identifiability Perspectivecited by 37
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  18. 2024A Sparsity Principle for Partially Observable Causal Representation Learningcited by 35
  19. 2023General Identifiability and Achievability for Causal Representation Learningcited by 34
  20. 2023Unpaired Multi-Domain Causal Representation Learningcited by 32
  21. 2022Partial Disentanglement via Mechanism Sparsitycited by 29
  22. 2023Predicting Ordinary Differential Equations with Transformerscited by 26
  23. 2021Discovering Sparse Interpretable Dynamics from Partial Observationscited by 25
  24. 2023Temporally Disentangled Representation Learning under Unknown Nonstationaritycited by 22
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  26. 2018Fast Gaussian Process Based Gradient Matching for Parameter Identification in Systems of Nonlinear ODEscited by 17
  27. 2024Mechanistic Neural Networks for Scientific Machine Learningcited by 16
  28. 2021Identifiability Analysis of Linear Ordinary Differential Equation Systems with a Single Trajectorycited by 10
  29. 2023On the Identifiability of Switching Dynamical Systemscited by 9
  30. 2023An Interventional Perspective on Identifiability in Gaussian LTI Systems with Independent Component Analysiscited by 9
  31. 2023Simultaneous identification of models and parameters of scientific simulatorscited by 8
  32. 2022On Finite-Sample Identifiability of Contrastive Learning-Based Nonlinear Independent Component Analysiscited by 7

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2024: 4; 2025: 11; 2026: 8.

23 papers.

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  1. 2024Unifying Causal Representation Learning with the Invariance Principlecited by 31
  2. 2024The Landscape of Causal Discovery Data: Grounding Causal Discovery in Real-World Applicationscited by 18
  3. 2025Prediction-Powered Causal Inferencescited by 9
  4. 2025Position: An Empirically Grounded Identifiability Theory Will Accelerate Self-Supervised Learning Researchcited by 9
  5. 2025Learning General Causal Structures with Hidden Dynamic Process for Climate Analysiscited by 7
  6. 2024Scalable Mechanistic Neural Networks for Differential Equations and Machine Learningcited by 5
  7. 2025Sanity Checking Causal Representation Learning on a Simple Real-World Systemcited by 5
  8. 2025Mechanistic PDE Networks for Discovery of Governing Equationscited by 4
  9. 2025The Third Pillar of Causal Analysis? A Measurement Perspective on Causal Representationscited by 4
  10. 2024Physically Interpretable World Models via Weakly Supervised Representation Learningcited by 3
  11. 2025Revealing Multimodal Causality with Large Language Modelscited by 3
  12. 2026Disentangling Dynamical Systems: Causal Representation Learning Meets Local Sparse Attentioncited by 3
11 more
  1. 2026Causal Representation Meets Stochastic Modeling under Generic Geometrycited by 2
  2. 2025"Cause" is Mechanistic Narrative within Scientific Domains: An Ordinary Language Philosophical Critique of "Causal Machine Learning"cited by 1
  3. 2025Towards Causal Representation Learning with Observable Sources as Auxiliariescited by 1
  4. 2025Learning Explicit Single-Cell Dynamics Using ODE Representationscited by 1
  5. 2025ROPES: Robotic Pose Estimation via Score-Based Causal Representation Learningcited by 0
  6. 2026Diverse Dictionary Learningcited by 0
  7. 2026No Epoch Like the Present: Robust Climate Emulation Requires Out-of-Distribution Generalisationcited by 0
  8. 2026Learning Individual Dynamics from Sparse Cross-Sectional Snapshotscited by 0
  9. 2026Disentangling Continuous-Time Latent Dynamics: Identifiability of Latent SDEs via Diffusion Shiftscited by 0
  10. 2026Identifying ODEs from Unstructured Data with Causal Representation Learningcited by 0
  11. 2026Identifiable World Models from Pretrained Diffusion Representationscited by 0